This invention relates to the measurement of thickness of a coating of a material on a substrate, and to the measurement and control of the rate of deposit of the material. The invention is more particularly directed to a method of measuring the amount of material being deposited upon a piezoelectric crystal by monitoring predetermined resonance frequencies and monitoring changes in those resonance frequencies.
Monitoring and controlling of the growth rate of thick or thin films, especially those deposited by vapor deposition or sputtering, is important in maintaining the quality of the devices produced in this manner. Quartz crystal deposition monitors have typically been employed for this purpose. Most usually, such monitors utilize the thickness shear wave mode of an AT-cut piezoelectric quartz crystal to monitor the rate of growth of thin films. In a typical arrangement, a quartz crystal with appropriate electrodes is placed in the feedback loop of a suitably designed oscillator circuit as a frequency control element. The equivalent electrical admittance of the quartz crystal is a maximum at its series resonance frequency, so the oscillator output tends to maintain itself at that frequency. Consequently, any change in the series resonance frequency of the crystal produces a corresponding change in the oscillator output frequency. The quartz crystal is physically positioned within an evaporation chamber or sputtering chamber where it is exposed to evaporants. As the evaporants condense on the surface of the quartz crystal, the mass of the crystal increases and its resonance frequency or frequencies decrease. While the quartz crystal can be made to oscillate in many different modes, the thickness shear wave mode is the most convenient for its mass-sensing properties.
The vibrating crystal is coated in proportion to the coating on other substrates in the chambers and the reduction in its resonance frequency on account of mass loading is indicative of the coating thickness on the crystal. Thus, the shift in crystal resonance frequency also indicates the coating thickness on the substrates. The resonance frequency is a highly sensitive measure of the applied coating thickness. Any changes in resonance frequency over time indicate the coating or deposition rate, i.e., change in thickness per unit time. Because the resonance frequency changes depend on the mass of the deposited material that has been added to the crystal, these quartz crystal monitors are often referred to as quartz crystal microbalances or microscales.
In a typical quartz crystal microbalance system, the useful lifetime of the sensing crystal is rather limited. The accumulation of deposition on the crystal surface reduces the sharpness and quality of the resonances, and sooner or later the crystal is no longer able to sustain vibration. At that time, the crystal must be replaced, or else controlled deposition cannot be continued. If crystal failure occurs during the deposition of a particular layer, it may be necessary to scrap the entire work product, with significant loss in investment to that point.
Various procedures to predict useful life until crystal failure has been proposed, e.g. as discussed in U.S. Pat. No. 4,817,430, so that the crystal can be replaced before its degradation can cause a problem. However, these techniques do not permit a degraded crystal to continue in use.
Current approaches to quartz crystal microbalances do not permit use of the same crystal to monitor and control the deposition of multiple layers of different materials. However, in many types of devices, such as multi-material optical devices or superconducting thin film devices, a sequence of layers must be laid down to rather precise specifications. In such applications, the conventional approach is to employ several multiple crystals in individually shuttered sensor heads, each head dedicated to a specific material, each head with its own tooling factor, and each crystal with its own resonance characteristics. Alternatively, it is possible in some processes to break vacuum, open the chamber, and change crystals for each layer of film. In either case, the expense and time constraints are high, and the processes are susceptible to operator error.
Operation of modern quartz crystal microbalances can be based on the so-called Lu-Lewis relation, which takes into account not only the mass density of the crystal, but also the acoustic impedance mismatch at the quartz-film interface. An example of this technique is "Z-match," a trademark of Leybold Inficon, Inc. This has resulted in improved performance, especially in the case of thick-film depositions. The Lu-Lewis relationship can be expressed simply as follows: ##EQU1## where f is the composite resonance frequency, f.sub.Q and f.sub.F are the mechanical resonance frequencies of the crystal and film, respectively, and Z.sub.Q and Z.sub.F are the specific acoustical impedances of the crystal and film, with respect to a piezoelectrically excited shear wave. This relation yields an explicit mass load versus frequency relation: ##EQU2## where M.sub.F and M.sub.Q are the areal mass densities of the film and the quartz crystal, respectively. This ratio is indicated by m in subsequent text.
The principal drawback to the use of this equation is the need to know the value of the acoustic impedance ratio Z=Z.sub.Q /Z.sub.F. This can be looked up for some bulk materials, but the effective Z value in films deposited at different rates or to different thicknesses or for films comprised of layers of several materials is not well known and is not entirely predictable.
As aforesaid, the acoustic impedance ratio, or Z-ratio, for the bulk material is often quite different from that of the thin film, which is more sensitive to process parameters. For many rather exotic materials, the Z-ratio is simply not known. In such cases it is possible to set the Z-ratio to unity, but this false premise introduces errors in thickness and rate measurements, the magnitude of the error depending on the departure of the true Z-value from unity, as well as on the film thickness.
In addition, the current "Z-match" approach is not capable of accurate measurement of thickness for multiple layers. While in principle a single Z-match technique could be applied to multiple layers where the acoustic impedance of each layer is known, in practice that technique is regarded as far too cumbersome to be implemented. See C. Lu and A. W. Czanderna, Applications of Piezoelectric Quartz Crystal Microbalances; Elsevier, N.Y. 1984. The complexity of the mathematical analysis increases rapidly in respect to the number of layers involved, so that it is less practical than to track the deposition process with multiple crystals, with only a single material being deposited on a specific crystal.
A previous approach using the acoustic impedance ratio, Z=Z.sub.Q /Z.sub.F, is to employ not only the quartz crystal fundamental frequency, but also a selected overtone or higher-frequency resonance. This approach is referred to as "Auto Z match." Typically, a quasiharmonic having approximately three times the fundamental frequency is used as the upper frequency. The two frequencies are sequentially applied to predict the impedance ratio or Z-ratio. The basics of this approach are discussed in E. Benes, Improved Quartz Crystal Microbalance Technique, J. Appl. Phys. 56, Aug. 1, 1984, pages 608 to 626.
Also with respect to the two-frequency method of measuring the effective Z ratio, as described in the Benes article, a two-frequency oscillator is needed to detect two resonance frequencies that are in the ratio of 1:3 or 1:5. This method also requires the simultaneous solution of two non-linear equations that may not always converge to a unique solution. Also, the required plano-plano-convex crystal two-frequency oscillator tends to be too noise-prone to be useful: the electrical admittance of the plano-convex crystal at higher quasi harmonic resonances drops off rather rapidly, approximately as the square of the frequency ratio, so that the sensitivity to a third-order resonance is at most one-ninth that of the fundamental. This makes it enormously difficult to obtain accurate readings of the higher frequency modes, especially as there are several quasi-harmonic and anharmonic modes situated close to one another on the frequency spectrum.
It has not previously been possible to find two distinct mass-load-sensitive vibrational modes for a given quartz crystal within a short period of time, and without the assurance of not being trapped on another mode. Also, it has been impossible to isolate in real time the various vibrational modes of a quartz crystal after there has been material deposited to the point at which the crystal resonance can no longer drive an oscillator.